Physical basis of the power-law spatial scaling structure of peak discharges

Key theoretical and empirical results from the past two decades have established that peak discharges exhibit power-law, or scaling, relation with drainage area across multiple scales of time and space. This relationship takes the form Q(A)= $#945;A^Θ where Q is peak discharge, A is the drainage area, Θ is the flood scaling exponent, and α is the intercept. Motivated by seminal empirical studies that show that the flood scaling parameters α and Θ change from one rainfall-runoff event to another, this dissertation explores how certain rainfall and catchment physical properties control the flood scaling exponent and intercept at the rainfall-runoff event scale using a combination of extensive numerical simulation experiments and analysis of observational data from the Iowa River basin, Iowa. Results show that Θ generally decreases with increasing values of rainfall intensity, runoff coefficient, and hillslope overland flow velocity, whereas its value generally increases with increasing rainfall duration. Moreover, while the flood scaling intercept is primarily controlled by the excess rainfall intensity, it increases with increasing runoff coefficient and hillslope overland flow velocity. Results also show that the temporal intermittency structure of rainfall has a significant effect on the scaling structure of peak discharges. These results highlight the fact that the flood scaling parameters are able to be estimated from the aforementioned catchment rainfall and physical variables, which can be measured either directly or indirectly using in situ or remote sensing techniques. The dissertation also proposes and demonstrates a new flood forecasting framework that is based on the scaling theory of floods. The results of the study mark a step forward to provide a physically meaningful framework for regionalization of flood frequencies and hence to solve the long standing hydrologic problem of flood prediction in ungauged basins.